TenMarks teaches you how to use the discriminant to solve problems on quadratic equations.
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Learn about Applications of the Discriminant Word problems, the heights above the ground of a model rocket on a particular launch can be modeled by the equation h=-4.9t²+102t+100, where t is the time in seconds. Will the rocket reach a height of 600 meters? Use the discriminant. So in this problem we need to check whether the rocket will reach height of 600 meters. So we need to plug in the height in this equation. So our equation says h=-4.9t²+102t+100 and then we’re going to go ahead and plug in h which is our height 600. So I'm going to go ahead and plug 600 in and that will equal -4.9t²+102t+100. Now, we need the write the equation in standard form, we need to make sure the equation written in standard from and remember standard form is ax²+bx+c=0. So we need to get this equation to equal 0, so I'm going to go ahead and subtract 600 from both sides which will give me 0=-4.9t²+102t++ (-500). So you could write it this was or you could write it as -4.9t²+102t+-500=0, so now it’s written in standard form. So now that we have it written in standard from we need to find our a, b and c. So a, b and c in this equation, so a in this equation is -4.9, b is 102 and c is -500. Now what we need to do is evaluate the discriminant and remember when it’s written in standard form your discriminant is b²-4ac, so this is the discriminant. So now, we’re going to plug this in to our discriminant so we’re going to have b²-4ac so that equals b is 102 so we’re going take 102²-4×a, which is -4.9×c, which is -500. So if we go ahead and solve this 102² is 10,404- and if I multiply this 4×4.9×500 I get 9800. And then if I go ahead and subtract these two numbers I get 604. So my discriminant is positive at 604 which is positive and remember that if the discriminant is greater than zero if it’s positive you have two real solutions. And if the discriminant is equal to 0 you have one real solution. And then, if the discriminant is less than 0 then you have no solutions, no real solutions. So since this discriminate is 604 it’s greater than zero, it’s positive than this equation has two real solutions, which means there are 2×t when the height h is 600. So the rocket will reach a height of 600 meters twice once on the way up and once on the way down. So, things to keep in mind, remember that the number solutions of the quadratic equation can be determine by evaluating your discriminant just like we did down here we evaluated our discriminant to find how many solutions we have. Also, if the quadratic equation is written in standard form it discriminant at b²-4ac. And if the discriminant is greater than zero or positive the equation has two real solutions. If the discriminant is equal to zero there's one real solution and if the discriminant is less than zero there are no real solutions.
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